Idioms – ‘From-Time-to-Time’ vs ‘From Time to Time’

I generally consider "idiomatic" and "idiom" to have approximately the same relationship that Damkerng T's comment suggests: an idiomatic construction is any construction that a native speaker would prefer for a given use, while an idiom is a set and rather quirky phrase or pattern that's unusual enough to identified and talked about by laymen, not just linguists. Conveniently, that's also the dictionary definition.

Basically, yes, the question phrase is idiomatic; it's not really (much of) an idiom, since it's not very odd or exceptional or memorable.

You can think of "see you" is a short form of "see you again soon". It doesn't matter whether you are currently with them, because you have probably seen them at some point before, even if you are not with them now, and it's about the next time you see them.

Arguably, you could still say it even if you expect your next contact to be by phone or email, because at some point after that you probably will meet them face to face again.

If you want to make it clear that you expect to be in contact with them by some other means (phone, email) then you can say:

Speak to you soon - for a phone or skype conversation
Looking forward to hearing from you soon - expecting a written communication

Note that the written form is rather more formal... it is more suitable to finish off an email than to say to somebody directly or by phone.

I have even heard expressions like "Skype you soon!".